The present invention generally relates to sampling frequency converters, and more particularly to a sampling frequency converter capable of converting (hereinafter referred to as a sampling frequency conversion) a first signal sampled at a first sampling frequency into a second signal sampled at a second sampling frequency.
In order to record a signal from a device operating at a predetermined sampling frequency with an apparatus for recording and reproducing a digital signal sampled at a sampling frequency different from the predetermined sampling frequency, a sampling frequency converter is used to convert the sampling frequency of the signal which is to be recorded, so that the sampling frequency of the signal which is to be recorded becomes equal to the sampling frequency of the recording and reproducing apparatus. Generally, the sampling frequency converter consists of an interpolation device supplied with an input signal, a filter supplied with the output of the interpolation device, and a decimation device supplied with the output of the filter.
For example, an input signal x.sub.n at a time nT which is sampled at a first sampling frequency f1 (where T indicates the sampling time, and n is an integer), is inserted with L-1 zeros (L is an integer greater than or equal to 1) at the above interpolation device. Accordingly, a signal w.sub.nL+i is produced from the interpolation device. This signal w.sub.nL+i can be described by an equation ##EQU1## Hence, a frequency spectrum of the above signal w.sub.nL+i obtained from the interpolation device becomes a frequency spectrum in which a frequency spectrum part up to a frequency f1/2 is symmetrically folded and distributed up to a frequency Lf1/2.
In order to extract the output signal w.sub.nL+i of the interpolation device at the decimation device in a manner such that every M-th (M is an integer greater than or equal to unity) signal is extracted and the signal is converted into a signal sampled at a second sampling frequency f2, a frequency spectrum part above the frequency f1/2 must be eliminated in the above frequency spectrum of the signal w.sub.nL+i. The above filter between the interpolation device and the decimation device is provided to eliminate this unwanted frequency spectrum part.
The signal obtained from the filter is sampled at the decimation device such that every M-th signal is extracted. Hence, an output signal y.sub.n sampled at the second sampling frequency f2 is thus obtained from the above decimation device. In this case, a relation f2/f1=L/M stands.
The above signal y.sub.n sampled at the second sampling frequency f2 can be described by an equation ##EQU2## where N is the order of the filter and h.sub.m is the impulse response of the filter. As clearly seen from this equation, the above signal y.sub.n is determined according to the performance of the filter. Thus, when designing the filter, there is a demand for the digital filter to have no aliasing (folding) distortion and no delay distortion. Further, it is desirable for the digital filter to have a simple circuit construction.
Therefore, in a case where the first sampling frequency f1 is smaller than the second sampling frequency f2, for example, a finite impulse response digital filter can be used as the above filter. However, due to the level of the present technology, the order of the filter became exceedingly high. In a case where the conversion ratio L/M=8/7, for example, the order of the filter became over 1,000. When the order of the filter becomes high, errors are easily introduced during mathematical operations. Moreover, delay distortion is easily introduced. Further, there is a disadvantage in that the size of the apparatus becomes large since the order of the filter is high. On the other hand, in a case where the conversion ratio is a small value such as L/M=1007/1001, for example, there were cases where a filter having a characteristic in which the passing band is one-half the frequency band of the sampling frequency for obtaining the maximum output, could not be realized. In addition, the order of the filter is reduced compared to the conventional filter when a so-called two-stage finite impulse response filter is used. However, there is still a limit to the extent the order of the filter can be reduced, and the order of the filter could not be reduced significantly.
On the other hand, in a case where the first sampling frequency f1 is larger than the second sampling frequency f2, for example, an infinite impulse response digital filter can be used. When the infinite impulse response digital filter is used to subject the signal to a decimation process, an output having a multiplication factor of 1/M was required as a result, for the sampled values extracted from every M-th signal. Accordingly, transfer functions of high order were required in both the numerator and the denominator of the transfer function equation describing the digital filter.